Applications for optical fiber transmission systems, wireless systems, or co-axial cable systems, there exist many approaches to probabilistic shaping, which can demonstrate a sub-optimal gain, such as shell-mapping and trellis coded modulation. In order to approach the maximum achievable gain, the best known method in the literature for probabilistic shaping is the use of a constant composition distribution matcher (CCDM), whereby every possible output sequence has the same per-symbol probability distribution and therefore the same “composition”. This method requires output sequence lengths on the order of thousands of symbols in order to achieve good performance. A significant problem with this method is that the only known mapping and demapping algorithms (which map and demap uniformly distributed input bits to shaped output sequences) operate sequentially on the input or output symbol sequence. Good performance is therefore only achieved at the cost of latency, which makes implementation in hardware impossible.
Accordingly, there is need to develop a low complexity method and system for matching and dematching these CCDM sequences.